The next generation of displays uses organic light-emitting diodes (OLEDs). Such displays make it possible to display darker blacks than liquid-crystal displays (LCDs), providing a significantly larger dynamic range. We performed photometric and psychophysical measurements with an OLED display. We found that the widely used tone curve with a gamma value of 2.2 does not produce equally discriminable luminance steps in these displays. In a 2-alternative, forced-choice psychophysical task, subjects discriminated the luminances of adjacent square patches. We used spatial dithering to create small apparent changes in luminance. We measured the minimum perceivable change in luminance for a range of luminances. From these discrimination thresholds, we estimated the tone curve and necessary number of discrete steps that would fully cover the dynamic range in threshold-sized steps. Compared to the conventional tone curve, our experimental tone curve has smaller luminance differences in the low range and greater luminance differences in the high range, in accordance with Weberâ€™s law. This suggests that the conventional 2.2-gamma tone curve suffers from quantization issues at low luminance values and loss of detail at high luminance values. The conventional tone mapping is reasonably effective when the display has a low dynamic range of 100:1, but as dynamic range is increased, the conventional mapping increasingly diverges from a perceptually uniform mapping, so 8-bit gray levels are increasingly inadequate. Our research suggests that image quality can be significantly improved by using higher dynamic range displays with tone-mapping functions and bit depth that are appropriate for that range.